Yes, I said name something it won’t fix. And don’t say a broken heart 
.
A broken limb.
A broken connecting rod.
Broken valve springs.
It’s really not the right tape to be used for ductwork. You should really use (either a very specific duct tape designated as suitable for the job or) foil tape meant specifically for the application.
Weird, huh ?
And duck tape won’t fix ducks.
Herpes?
It’ won’t fix me breakfast. 
It can’t fix stupid.
Might be useful for a splint though!
I suspect that depends upon what is wrong with the duct.
Could probably make a decent cast out of duct tape too.
But duct tape only fixes things that are loose but should be tight.
For things that are tight but should be loose, WD-40.
Global warming.
Something that’s supposed to come apart, but is stuck.
My old homeowner advice from years ago:
“If it moves, but shouldn’t - duct tape. If is doesn’t move, but should - WD-40”.
Argh, got ninja’d twice while adding to my post 
I won’t, but the Bee Gees did…
Of course duct tape won’t fix everything. Everyone knows to fix everything you need both duct tape and WD-40.
If it moves when it shouldn’t, use duct tape.
If it doesn’t move when it should, use WD-40.
Edit: Missed the post by @snowthx that said the same thing. Oops.
Anything with a slippery coating like a car bumper taped to a well waxed trunk lid.
I hate duct tape. It leaves an almost unremovable residue especially if left in place for any duration, the vinyl backing tends to stretch rather than tear quickly, and is used inappropriately as a structural fix-all that fails suddenly. For the applications it is suited, i.e. as adhesive tape I much prefer gaffer tape which tears cleanly and leaves little residue. If you actually want to bond things together structurally or stop leaks JB Weld is a far superior method to tape.
Stranger
Not quite the same, but I badly sprained my right foot big toe a few days before embarking on a fairly epic hike an 800m ascent followed by 5 days in a river ( kloofing, as it is locally known ).
I really wanted that hike, so I duct-taped my big toe to my second and set off. I made it through the 5 days with regular painkillers and some whisky